Physical information

In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics (i.e. quantum information) is important, for example in the concept of quantum entanglement to describe effectively direct or causal relationships between apparently distinct or spatially separated particles.

Information itself may be loosely defined as "that which can distinguish one thing from another". The information embodied by a thing can thus be said to be the identity of the particular thing itself, that is, all of its properties, all that makes it distinct from other (real or potential) things. It is a complete description of the thing, but in a sense that is divorced from any particular language.

When clarifying the subject of information, care should be taken to distinguish between the following specific cases:

The above usages are clearly all conceptually distinct from each other. However, many people insist on overloading the word "information" (by itself) to denote (or connote) several of these concepts simultaneously. (Since this may lead to confusion, this article uses more detailed phrases, such as those shown in bold above, whenever the intended meaning is not made clear by the context.)

The instance of information that is contained in a physical system is generally considered to specify that system's "true" state. (A realist would assert that a physical system always has a true state of some sort—whether classical or quantum—even though, in many practical situations, the system's true state may be largely unknown.)

When discussing the information that is contained in physical systems according to modern quantum physics, we must distinguish between classical information and quantum information. Quantum information specifies the complete quantum state vector (or equivalently, wavefunction) of a system, whereas classical information, roughly speaking, only picks out a definite (pure) quantum state if we are already given a prespecified set of distinguishable (orthogonal) quantum states to choose from; such a set forms a basis for the vector space of all the possible pure quantum states (see pure state). Quantum information could thus be expressed by providing (1) a choice of a basis such that the actual quantum state is equal to one of the basis vectors, together with (2) the classical information specifying which of these basis vectors is the actual one. (However, the quantum information by itself does not include a specification of the basis, indeed, an uncountable number of different bases will include any given state vector.)

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